OCD metrology, also known as scatterometry, is a rapidly evolving technique for non-destructive dimension metrology utilized for in-line dimensional characterization of fabricated device structures. In the semiconductor industry for example, test grating structures may be fabricated along with the semiconductor device structures and these test grating structures may be optically characterized as a means of monitoring the fabrication processing.
Generally, OCD metrology entails simulating electromagnetic spectral information and comparing the simulated spectral information with measured spectral information collected from a sample grating illuminated on a workpiece (e.g., semiconductor wafer). As shown in FIG. 1, for an OCD metrology tool 100, the measured spectral information derived from the detector 110 is a result of the numerical aperture (NA) of the lens(es) 115 in the optical path which define a range of polar and azimuthal angles of incidence (θ, φ) over which the optical system 116 operates. As shown in FIG. 1, the angular spectrum may be decomposed into rays about a chief ray (defined at θ=θ0 and φ=0) which are then each modeled as a plane wave to produce a scattering function S(θ,φ) through rigorous computation of a diffraction scattering matrix by a technique such as rigorous coupled wave analysis (RCWA).
Because RCWA calculations are computationally intensive, it is advantageous to average the optical signature over sampled incident directions. Generally, averaging of the optical signature entails integrating over an aperture (circular, rectangular, or otherwise). Such integration can be estimated by numerical quadrature using a technique such as Gaussian quadrature (1D) or cubature (2D) in which a weighted sum of a function is evaluated at n selected points (nodes) xi within the aperture space Σi=1n wif (xi) as an approximation of ∫abf(x)dx, where each computation of f(xi) entails the intensive RCWA calculation.
For computing the nodes xi and weights wi of Gaussian quadrature (cubature) rules, the integrand function is preferably smooth. However, as a function of the illumination wavelength, numerical aperture, and dimensions of the grating, one or more Rayleigh singularities may occur within the numerical aperture space. Such a condition is also known as a Wood anomaly. Where Wood anomalies are not considered during numerical integration, convergence behavior for the numerical aperture average may be above measurement precision and/or be disadvantageously slow.
With smaller spot sizes often desirable for reducing the area of the workpiece 120 occupied by a target grating 125, a larger numerical aperture is desirable and Wood anomalies become more frequent. Techniques specially designed to integrate a numerical aperture spanning a Wood anomaly can therefore advantageously improve the simulated spectral information used in OCD measurement.